Saved Bookmarks
| 1. |
In the adjoining figure, ABCD is a trapezium in which CD || AB and its diagonals intersect at O. If AO = (5x – 7) cm, OC = (2x + 1) cm, BO = (7x – 5) cm and OD = (7x + 1) cm, find the value of x. |
|
Answer» From given statement: In Δ ADC EO || AB || DC By thales theorem: AE/ED = AO/OC …(1) In Δ DAB, EO || AB So, By thales theorem: DE/EA = DO/OB …(2) From (1) and (2) AO/OC = DO/OB (5x – 7) / (2x + 1) = (7x-5) / (7x+1) (5x – 7)(7x + 1) = (7x – 5)(2x + 1) 35x2 + 5x – 49x – 7 = 14x2 – 10x + 7x – 5 35x2 – 14x2 – 44x + 3x – 7 + 5 = 0 21x2 – 42x + x – 2 = 0 21(x – 2) + (x – 2) = 0 (21x + 1)(x – 2) = 0 Either (21x + 1) = 0 or (x – 2) = 0 x = -1/21 (does not satisfy) or x = 2 => x = 2. |
|